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Value of a composite function at a given point

This type of question, asked 4 times: 9 May 2024 S1, 12 May 2024 S2, 17 Apr 2026 S1, 19 Apr 2026 S1. All 4 questions below, oldest first.

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  1. Question 1

    9 May 2024 S1

    122
    If f:R−{−35}→Rf:\mathbb{R}-\left\{-\frac{3}{5}\right\}\to\mathbb{R} is defined by f(x)=3x−25x+3f(x)=\frac{3x-2}{5x+3}, then f∘f(1)f\circ f(1) is

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  2. Question 2

    12 May 2024 S2

    126
    If f(x)=x2+1f(x) = x^2+1 and g(x)=1xg(x) = \frac{1}{x}, then the value of f(g(g(f(x))))f(g(g(f(x)))) at x=1x = 1 is

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  3. Question 3

    17 Apr 2026 S1

    69
    If f:R→Rf : R \to R and g:R→Rg : R \to R are defined as f(x)=2x−∣x∣f(x) = 2x - |x| and g(x)=2x+∣x∣g(x) = 2x + |x|, then

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  4. Question 4

    19 Apr 2026 S1

    70
    If f(x)=x2f(x) = x^2 and g(x)=[x2]g(x) = [x^2] where [⋅][\cdot] represents the greatest integer function then, (f∘g)(32)+(g∘f)(32)(f \circ g)\left(\dfrac{3}{2}\right) + (g \circ f)\left(\dfrac{3}{2}\right) is equal to ...

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